Federal law enforcement officers are trying to determine whether they have uncovered a network of Al Qaeda supporters in Northern California.

Two law enforcement sources have confirmed to FOX News that there is a connection between Umer and Hamid Hayat, the father and son arrested over the weekend in Lodi, Calif., on criminal charges, and two Pakistani citizens currently being held on immigration violations. Lodi is an agricultural community 40 miles south of Sacramento.

The son allegedly received terrorist training and funding from the father, an ice cream truck driver, so he could carry out attacks on hospitals and large food stores in the United States.

Hamid Hayat, 22, and his father, Umer Hayat, 47, are charged with lying to authorities about the son's alleged training at an Al Qaeda (search) camp in 2003 and 2004 and money sent for training. Charges for terrorism could come soon.

Click here to view the criminal complaint. (FindLaw)

Umer and Hamid Hayat are American citizens, and the younger man was born in California.

On Monday, U.S. Immigration and Customs Enforcement (ICE) agents also arrested Mohammed Adil Khan, Shabbir Ahmed and another man for immigration violations. Khan is a citizen of Pakistan who is affiliated with the Farooqia Islamic Center near Lodi, Calif. Ahmed is a citizen of Pakistan who currently functions as the Imam of the Lodi Mosque. The Web site for the Farooqia Islamic Center in Lodi identifies both men as imams.

Those three men are expected to eventually appear before an immigration judge.

An FBI affidavit says Hamid Hayat first denied any link to terror camps, but then told agents he attended an Al Qaeda camp in Pakistan for six months.

A law enforcement source confirmed to FOX News that search warrants have been executed at two mosques, homes of the Hayats, as well as that of the Lodi Muslim Mosque's imam. The case is now described as "ongoing investigation by the JTTF," the joint terrorism task force. FOX News was told that the connection between the Hayat's and Khan Ahmed "is more than just a meeting, there are many connections, here and possibly Pakistan."

Taj Kahn, a spokesman for the Muslim community in Lodi, said the men had been targeted unfairly. "They have not violated any of the laws. They have not done anything wrong to give us any suspicions," Kahn said during a morning press conference.

"We love this country. We are here to stay. We are part of this country. We are going to work together to solve all our problems."

Both men were being held at the Sacramento County Jail. Umer Hayat's attorney, Johnny Griffin III, called the allegations "shocking" but said his client "is charged with nothing more than lying to an agent."

U.S. Magistrate Judge Peter A. Nowinski denied a bail request for the elder Hayat, saying he was a flight risk and a danger to the community.

"He just returned from Pakistan where he built a new home and contributed financial assistance to an Al Qaeda sponsored program training his son and others to kill Americans whenever and wherever they can be found," Nowinski said.

Agents removed boxes of photographs, videocassettes and fax machines were removed from the Hayat home over the weekend.

Hamid Hayat's attorney wasn't in court, and Nowinski set his bail hearing for Friday.

"Hamid advised that he specifically requested to come to the United States to carry out his jihadi mission," according to the affidavit. "Potential targets for attack would include hospitals and large food stores."

Iraq, Afghanistan and the disputed Kashmir region were among other locales camp attendees could choose to carry out their missions, according to what Hamid Hayat told agents.

The affidavit discusses weapons training Hamid Hayat received and says, "during his weapons training, photos of various high ranking U.S. political figures, including President Bush, would be pasted onto their targets."

Umer Hayat told agents his son first became interested in attending terror training camps during his early teenage years.

According to reports in the Los Angeles Times and The Sacramento Bee , Hamid Hayat was trying to return to the United States from Pakistan on May 29 when the FBI told its Sacramento office that he was on the federal "no-fly" list.

The plane was diverted to Japan, where Hayat was interviewed by the FBI and denied any connection to terrorism. He was allowed to fly to California, but was interviewed again on June 3-4. He then acknowledged spending time at the training camp, the affidavit said.

He voluntarily took a lie detector test, which the affidavit said indicated he was not telling the truth. Hayat then acknowledged spending time at the training camp, the affidavit said.

FOX News' Claudia Cowan, Catherine Herridge and The Associated Press contributed to this report.